It is perfectly safe, this is why Steam created this API at all. All you share is your Steam ID, and that is public already.

That said, you should be aware and sign in through official steam community site only ( https://steamcommunity.com/oauth/login?client_id= ). Scammers might try to falsify it and look exactly same way to get you credentials, but address will be different. This is why you should also use Steam Guard as a second line of defence.

Hi.

I can assure you it's perfectly safe as we just keep public information in our database: avatar, screen name, steam id. We need those information to then grant you free things on steam and track your achievements for unlocking special badges. 

If you have more question don't hesistate to ask, we'll gadly assist you.

EDIT: Also Sublustris is right, when other website want you to steamconnect you should verify the url you are on and verify that it's the legit one.